At the middle-school level students study the meanings of operations
and how operations relate to each other, and learn to compute
fluently and make reasonable estimates. They deepen their
understandings of fractions, decimals, and percents, and learn to
understand ratio and proportion using methods such as scaling and
finding equivalent ratios. Students work with large numbers,
exponents, and scientific notation, and practice using factors,
multiples, prime factorization, and relatively prime numbers.

For background information elsewhere on our site, explore the
Middle School
area of the Ask Dr. Math archives. To find relevant
sites on the Web, browse and search
Arithmetic/Early
Mathematics in our Internet Mathematics Library; to find
middle-school sites, go to the bottom of the page, set the searcher
for middle school (6-8), and press the Search button.

Pre-Algebra, difficulty level 3. Duke's head is 6 inches long, his tail is as long as his head plus half the length of his body, and his body is as long as the head and tail combined. How long is Duke?
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Pre-Algebra, difficulty level 2. Ms. Nelson claims that she is three times as old as her little sister. However, six years ago she was five times as old as her sister was. How old is Ms. Nelson?
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Math Fundamentals, difficulty level 3. Fred put his football down on a goal line of the 100-yard field. He then moved it forward half the field distance, over and over again. When did the distance first become less than one inch?
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Math Fundamentals, difficulty level 3. The label on the lemon concentrate says that I need to mix 2 cups of concentrate with 3 cups of water. How much lemon concentrate should I buy to make 25 gallons of lemonade?
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Pre-Algebra, difficulty level 3. The first student says his/her own name; the second student repeats the first student's name and adds his/her own name... How many names are said if the numbers of students in my math classes on the first day are 27, 28, 32, 31, and 30?
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Pre-Algebra, difficulty level 3. Peanut, the overexcited dog, makes 40 laps around a stake and travels a total distance of 1 mile. If his bowl of water is 20 feet away from the stake, can he get a drink?
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Pre-Algebra, difficulty level 3. Four new students arrive in Mrs. Brown's homeroom. After a few minutes she turns to them and says, "There are 1680 ways
that you can sit in the empty seats." How many empty seats are there in the room?
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Math Fundamentals, difficulty level 1. The product of 3 and 24 is 72. The sum of 3 and 24 is 27, which is the reverse of 72. Can you find other pairs of numbers such that their product is the reverse of their sum?
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